Abstract. Mathematical analysis of the Anderson localization has been
facilitated by the use of suitable fractional moments of the Green
function. Related methods permit now a readily accessible derivation
of a number of physical manifestations of localization, in regimes
of strong disorder, extreme energies, or weak disorder away from the
unperturbed spectrum. The present work establishes on this basis
exponential decay for the modulus of the two-point function, at all
temperatures as well as in the ground state, for a Fermi gas within
the one-particle approximation. Different implications, in particular
for the Integral Quantum Hall Effect, are reviewed.